Lean is a new open source theorem prover being developed at Microsoft Research and
Carnegie Mellon University, with a small trusted kernel based on dependent type theory. It …

Despite the success of large language models (LLMs), the task of theorem proving still
remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods …

A FORMAL PROOF OF THE KEPLER CONJECTURE Page 1 Forum of Mathematics, Pi (2017),
Vol. 5, e2, 29 pages doi:10.1017/fmp.2017.1 1 A FORMAL PROOF OF THE KEPLER …

Abstract The Thousands of Problems for Theorem Provers (TPTP) problem library is the
basis of a well known and well established infrastructure that supports research …

We propose a deep learning-based approach to the problem of premise selection: selecting
mathematical statements relevant for proving a given conjecture. We represent a higher …

Rigorous estimation of maximum floating-point round-off errors is an important capability
central to many formal verification tools. Unfortunately, available techniques for this task …

This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and
software design and verification, unexpected mathematical beauty. The lambda calculus …

Hammers provide most powerful general purpose automation for proof assistants based on
HOL and set theory today. Despite the gaining popularity of the more advanced versions of …

Real analysis is pervasive to many applications, if only because it is a suitable tool for
modeling physical or socio-economical systems. As such, its support is warranted in proof …

Techniques combining machine learning with translation to automated reasoning have
recently become an important component of formal proof assistants. Such" hammer" tech …